On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere.

Let M be a compact hypersurface with constant mean curvature in . Denote by H and S the mean curvature and the squared norm of the second fundamental form of M, respectively. We verify that there exists a positive constant γ(n) depending only on n such that if ∣H∣ ⩽ γ(n) and , then S ≡ β(n, H) and M is a Clifford torus. Here, . [ABSTRACT FROM AUTHOR]